The Weak Extension Principle and Its Coarse Version

A lecture by Alessandro Vignati explores the weak Extension Principle (wEP) and its coarse version as part of the Workshop on "Structures in Banach Spaces" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) in March 2025. Delve into Farah's formulation of the wEP from the late 90s, which aims to completely understand continuous functions between Čech-Stone remainders of zero-dimensional topological spaces. Learn why this principle doesn't follow from standard ZFC Axioms and is false under the Continuum Hypothesis, while certain instances can be derived from milder axioms like the Open Colouring Axiom and Martin's Axiom. Discover generalizations of the wEP to all Čech-Stone remainders of locally compact metrizable spaces and examine a coarse geometric version that yields rigidity results for Higson coronas and boundary spaces in coarse geometry under reasonable set theoretic assumptions. This 44-minute mathematical exploration offers advanced insights into topological spaces and their properties.